Cannonballs, jackknifes, belly flops, and pencil dives are all examples of simple tricks one can execute off a diving board. But why does a cannonball or jackknife make a bigger splash than pencil dives or belly flops? Furthermore, why do heavier-set people produce a higher splash than lighter people? How does a person’s weight affect splash height?
One study done by Brigham Young University showed high-speed images, revealing how splashes work1. When objects enter water they create a pocket of air that collapses from the pressure. The point at which the air pocket is collapsed, after it achieves an hourglass shape, is known as the pinch off point. This point is responsible for the noise or clap of the splash. When the water finally collapses it hits it’s self it still contains force, which is expressed in a spout of water that shoots up from the area where the air pocket existed.
In the Olympics, divers strive to have very little splash upon entering the pool. The reason for this being the judges take splash size into account when scoring a dive. To minimize the size and height of their splashes, divers attempt to enter the water vertically in a long straight form. This form will make it so that when the pinch off point of the divers air pocket collapses it hits the diver negating the energy that would shoot the water upwards into the diver2.
Our experiment is to determine the effect of mass and surface area on height of the jet of water produced when an object is dropped in water. In examining mass, we use tennis balls of different weights to keep surface area/size constant. In examining surface area, we use a wooden block and a tennis ball of the same mass. We predict that the objects of greater mass will make deeper air pockets and thereby, higher splashes. We predict that objects of a smaller surface area will have a greater overall splash size (because of the larger initial contact area) but shorter splash height because the air pocket formed will be shallow.
Procedure
Five tennis balls were filled with sand and gravel in various increments (1. all sand, 2. half sand, 3. all gravel, 4. half gravel, 5. half gravel, half sand). We cut a hole with an X-acto knife, used a funnel to fill the balls, and then taped over the hole with duct tape. Mass was recorded using a balance.
We made a mark 7.62 cm (3 in) from the top edge of an 18.9 L (5 gallons) bucket. The bucket up was filled with water to that point. We set the bucket next to a brick wall and taped a meter stick upright against the wall for scale (from the ground up). The tennis balls were dunked in water first to ensure consistency among drops.
Video analysis on Logger Pro was used to capture the splash and record the height. The laptop was position so that the entire meter stick and bucket were in the frame.
One person dropped the ball from the top of meter stick each trial. When the person recording on the laptop said "go", the video capture was initiated and other person dropped the ball directly over the bucket, aiming for the center each time. The ball was also oriented so that the taped hole was on top for each drop. The video was stopped when the splash was over.
We dropped each of the balls 3-5 times. After each drop, the video was analyzed and the splash height was measured by selecting the highest water droplet seen in the footage. Position on the Y-axis was recorded. After each drop, we also refilled the bucket to the marked level.
We repeated the following procedure with a tennis ball and wooden block of the same mass. Surface area was measured and recorded. Instead of 3-5 trials, we dropped the objects 10 times each.
Results
Effect of Mass on Splash Height
Mass (g)
Average Height (m)
111.1
1.597
113.9
1.73
164.1
1.475
176.7
1.658
185.4
1.76
Linear fit (all data points): .000165x+1.619
r = .0511
Quadratic fit (all data points): .00021x^2-.061+5.87
RMSE = 0.0568
Linear fit (last three data points): .01346x-0.7302
r = 0.998
Effect of Surface Area on Splash Height
Ball (153.9 cm^2)
Wooden Block (263.5 cm^2)
Height (m)
Height (m)
1.651
0.8797
1.991
0.6324
1.310
0.7726
1.843
0.8205
1.418
0.8819
1.491
0.7975
1.877
0.7680
1.253
0.6169
1.376
0.6388
1.419
0.7766
Avg=1.56
Avg = 0.758
We performed a T-test on the height values for the two objects of different surface area.
p = .00000129
Conclusion
There does not appear to be a clear relationship between mass and height when examining the data points as a whole. The correlation (r) from a linear regression of mass and height gives us a value of only .0511. If we perform a quadratic regression, a root-mean-square-error (RMSE) of 0.0568 is given. Since, an RMSE (a measure of how far off the curve's estimation is) of 0 is ideal, a quadratic relationship is not a bad indicator of the relationship. However. a quadratic relationship between mass and splash height does not make practical sense. For our quadratic mean, that would mean at a mass of 145.5 g the height reaches a minimum. There is no physical explanation for this phenomena other than experimental error.
If we strike out the first two data points, a strongly-correlated linear regression can be made. y=.01346x-0.7302 gives us a correlation (r) of 0.998. Since the slope is positive, for these three points we can infer that mass and height are directly proportional.
Our test gave us a p-value .00000129, suggesting that our results are statistically significant since p < .05 and that there is a statistically significant difference between the splash heights of both surface areas. The difference could not have happened by chance alone (or there is only a .000129% chance that it did). Thus, we can conclude not only that surface area does affect the height of the splash, but also that objects of smaller surface area produce a higher splash. Presumably the air pocket formed by the objects of surface area is deeper and can therefore displace a higher jet of water. Also, the object of greater surface hits the a greater area of water upon contact and therefore produces a broader, scattered splash. Thus, its jet will not reach as high.
We first became interested in this project when discussing the difference between a cannonball dive and a belly flop and why these dives produced markedly different splashes. We can infer from our data that the cannonball will make a higher vertical splash than the belly flop because the air cavity formed is deeper probably influenced by a smaller initial area of contact. We can also conclude that a person of greater mass will produces a higher vertical splash.
Like many experiments, ours is not devoid of human error and flaws. One of the inconsistencies of this experiment was the drop release and positioning. While we used the same person to drop the ball/block each trial, we found that the same object's impact on the water varied considerably each time. If the person dropping the ball ensures that each drop begins at the top of meter stick, with the taped side up, and in the center of bucket than the error may be reduced. In our experiment, the ball did not always hit the center of the bucket. Also, in a few of our trials, we may have neglected to fill the water bucket back up to the marked level. With less water inside the bucket, the splash height could have feasibly been decreased.
We have may benefited from using more balls of different masses, especially to validate the linear relationship we found. Three points are sufficient to make a line, but we would have greater confidence with 5 points or more.
One concern that came up was if the ability of the wooden block to float had any effect on the splash height and therefore confounding of variables. Only the lightest tennis ball (filled halfway with sand) floated. However, it may be ideal to use an object that floats because human bodies naturally float in water as well.
As a suggestion for the future, a camera of relatively higher resolution (than the Macbook cameras) is preferable. Often the highest water droplets were hard to spot with the quality of the video in Logger Pro.
A question that could be addressed is how drop height affects the splash height. Also, we only used two different objects for surface area. It would be interesting to test other shapes such as a cylinder and a cone. What about object density? Surface texture (smooth, rough, bumpy, etc.)? All of these possible experiments will lead us to a more comprehensive study of the physics of a splash.
5. Litchmen, Flora. "High-Speed Video Reveals Physics Of Splashes." NPR : National Public Radio : News & Analysis, World, US, Music & Arts : NPR. Nation Public Radio, 6 Feb. 2009. Web. 24 Jan. 2012. <http://www.npr.org/templates/story/story.php?storyId=100333707>.
Table of Contents
Effect of Surface Area and Mass on Splash Height
Emmy, Daniel
Introduction
Cannonballs, jackknifes, belly flops, and pencil dives are all examples of simple tricks one can execute off a diving board. But why does a cannonball or jackknife make a bigger splash than pencil dives or belly flops? Furthermore, why do heavier-set people produce a higher splash than lighter people? How does a person’s weight affect splash height?
One study done by Brigham Young University showed high-speed images, revealing how splashes work1. When objects enter water they create a pocket of air that collapses from the pressure. The point at which the air pocket is collapsed, after it achieves an hourglass shape, is known as the pinch off point. This point is responsible for the noise or clap of the splash. When the water finally collapses it hits it’s self it still contains force, which is expressed in a spout of water that shoots up from the area where the air pocket existed.
In the Olympics, divers strive to have very little splash upon entering the pool. The reason for this being the judges take splash size into account when scoring a dive. To minimize the size and height of their splashes, divers attempt to enter the water vertically in a long straight form. This form will make it so that when the pinch off point of the divers air pocket collapses it hits the diver negating the energy that would shoot the water upwards into the diver2.
Our experiment is to determine the effect of mass and surface area on height of the jet of water produced when an object is dropped in water. In examining mass, we use tennis balls of different weights to keep surface area/size constant. In examining surface area, we use a wooden block and a tennis ball of the same mass. We predict that the objects of greater mass will make deeper air pockets and thereby, higher splashes. We predict that objects of a smaller surface area will have a greater overall splash size (because of the larger initial contact area) but shorter splash height because the air pocket formed will be shallow.
Procedure
Five tennis balls were filled with sand and gravel in various increments (1. all sand, 2. half sand, 3. all gravel, 4. half gravel, 5. half gravel, half sand). We cut a hole with an X-acto knife, used a funnel to fill the balls, and then taped over the hole with duct tape. Mass was recorded using a balance.
We made a mark 7.62 cm (3 in) from the top edge of an 18.9 L (5 gallons) bucket. The bucket up was filled with water to that point. We set the bucket next to a brick wall and taped a meter stick upright against the wall for scale (from the ground up). The tennis balls were dunked in water first to ensure consistency among drops.
Video analysis on Logger Pro was used to capture the splash and record the height. The laptop was position so that the entire meter stick and bucket were in the frame.
One person dropped the ball from the top of meter stick each trial. When the person recording on the laptop said "go", the video capture was initiated and other person dropped the ball directly over the bucket, aiming for the center each time. The ball was also oriented so that the taped hole was on top for each drop. The video was stopped when the splash was over.
We dropped each of the balls 3-5 times. After each drop, the video was analyzed and the splash height was measured by selecting the highest water droplet seen in the footage. Position on the Y-axis was recorded. After each drop, we also refilled the bucket to the marked level.
We repeated the following procedure with a tennis ball and wooden block of the same mass. Surface area was measured and recorded. Instead of 3-5 trials, we dropped the objects 10 times each.
Results
Effect of Mass on Splash Height
r = .0511
Quadratic fit (all data points): .00021x^2-.061+5.87
RMSE = 0.0568
Linear fit (last three data points): .01346x-0.7302
r = 0.998
Effect of Surface Area on Splash Height
p = .00000129
Conclusion
There does not appear to be a clear relationship between mass and height when examining the data points as a whole. The correlation (r) from a linear regression of mass and height gives us a value of only .0511. If we perform a quadratic regression, a root-mean-square-error (RMSE) of 0.0568 is given. Since, an RMSE (a measure of how far off the curve's estimation is) of 0 is ideal, a quadratic relationship is not a bad indicator of the relationship. However. a quadratic relationship between mass and splash height does not make practical sense. For our quadratic mean, that would mean at a mass of 145.5 g the height reaches a minimum. There is no physical explanation for this phenomena other than experimental error.
If we strike out the first two data points, a strongly-correlated linear regression can be made. y=.01346x-0.7302 gives us a correlation (r) of 0.998. Since the slope is positive, for these three points we can infer that mass and height are directly proportional.
Our test gave us a p-value .00000129, suggesting that our results are statistically significant since p < .05 and that there is a statistically significant difference between the splash heights of both surface areas. The difference could not have happened by chance alone (or there is only a .000129% chance that it did). Thus, we can conclude not only that surface area does affect the height of the splash, but also that objects of smaller surface area produce a higher splash. Presumably the air pocket formed by the objects of surface area is deeper and can therefore displace a higher jet of water. Also, the object of greater surface hits the a greater area of water upon contact and therefore produces a broader, scattered splash. Thus, its jet will not reach as high.
We first became interested in this project when discussing the difference between a cannonball dive and a belly flop and why these dives produced markedly different splashes. We can infer from our data that the cannonball will make a higher vertical splash than the belly flop because the air cavity formed is deeper probably influenced by a smaller initial area of contact. We can also conclude that a person of greater mass will produces a higher vertical splash.
Like many experiments, ours is not devoid of human error and flaws. One of the inconsistencies of this experiment was the drop release and positioning. While we used the same person to drop the ball/block each trial, we found that the same object's impact on the water varied considerably each time. If the person dropping the ball ensures that each drop begins at the top of meter stick, with the taped side up, and in the center of bucket than the error may be reduced. In our experiment, the ball did not always hit the center of the bucket. Also, in a few of our trials, we may have neglected to fill the water bucket back up to the marked level. With less water inside the bucket, the splash height could have feasibly been decreased.
We have may benefited from using more balls of different masses, especially to validate the linear relationship we found. Three points are sufficient to make a line, but we would have greater confidence with 5 points or more.
One concern that came up was if the ability of the wooden block to float had any effect on the splash height and therefore confounding of variables. Only the lightest tennis ball (filled halfway with sand) floated. However, it may be ideal to use an object that floats because human bodies naturally float in water as well.
As a suggestion for the future, a camera of relatively higher resolution (than the Macbook cameras) is preferable. Often the highest water droplets were hard to spot with the quality of the video in Logger Pro.
A question that could be addressed is how drop height affects the splash height. Also, we only used two different objects for surface area. It would be interesting to test other shapes such as a cylinder and a cone. What about object density? Surface texture (smooth, rough, bumpy, etc.)? All of these possible experiments will lead us to a more comprehensive study of the physics of a splash.
References
1. Truscott, Tadd. "The Anatomy of a Splash: High-Speed Photo Gallery." Popular Mechanics. Hearst Communication, Inc., n.d. Web. 22 Jan. 2012. <http://www.popularmechanics.com/outdoors/sports/physics/anatomy-of-a-splash-photo-gallery>.
2. Phan Son, Dang. "Size of the Splash Report." Scribd. Scribd Inc., 21 Oct. 2010. Web. 24 Jan. 2012. <http://www.scribd.com/doc/39824405/Size-of-the-Splash-Report>.
3. Orcutt, Mike. "Physics of a Cannonball Splash - How to Make the Biggest Splash." Popular Mechanics. 21 July 2010. Web. <http://www.popularmechanics.com/outdoors/sports/physics/physics-of-cannonball-splash>
4. Sauer, Rachel, and Dan Neal. "A Summer Cannonball Experiment." West Palm Beach News - Breaking News, Local Headlines & Weather | The Palm Beach Post. The Palm Beach Post, 29 July 2006. Web. 24 Jan. 2012. <http://www.palmbeachpost.com/accent/content/accent/epaper/2006/07/29/a1d_cannonball_0729.html>.
5. Litchmen, Flora. "High-Speed Video Reveals Physics Of Splashes." NPR : National Public Radio : News & Analysis, World, US, Music & Arts : NPR. Nation Public Radio, 6 Feb. 2009. Web. 24 Jan. 2012. <http://www.npr.org/templates/story/story.php?storyId=100333707>.